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Hermite Polynomial Based Expansion of European Option Prices

49 Pages Posted: 8 Nov 2010 Last revised: 20 Dec 2013

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: December 2013

Abstract

We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no requirements for affine dynamics or explicit characteristic functions. Moreover, convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices, in contrast with small-time asymptotic expansions in the literature. With closed-form expansions, we explicitly translate model features into option prices, such as mean-reverting drift and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach and its advantage over alternative expansion methods.

Keywords: Option Valuation, Closed-Form Expansion, Mean-Reversion, Self-Exciting Jumps, Double Exponential Jumps

JEL Classification: G12, C51

Suggested Citation

Xiu, Dacheng, Hermite Polynomial Based Expansion of European Option Prices (December 2013). Chicago Booth Research Paper No. 11-40. Available at SSRN: https://ssrn.com/abstract=1704588 or http://dx.doi.org/10.2139/ssrn.1704588

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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